Seeming paradox regarding conservation of angular momentum Two equal mass astronauts in space are holding hands: one's right hand with the other's left hand and left with right. They are facing each other and are stationary. Astronaut A pulls with her right hand B's left hand toward herself. While at the same time, B pulls on A using her right hand to draw A's left hand toward herself.The two astronauts begin to rotate about a central axis passing through the space between them. 
I know that angular momentum conservation is true at all times however, in this situation i am unable to explain it. The rotation of the astronauts implies that initially though $\vec L$ was zero about the central axis; that's not the case anymore. How do i resolve this? Is there a fault regarding the non-rigidity of the system?
 A: 
The two astronaut begin to rotate about a central axis passing through the space between them.

That's the part you're getting wrong.  There's no reason for this to happen.  The astronauts could (using some other method) momentarily transfer angular momentum between each other, so that one spins clockwise while the other spins counterclockwise, for example.  But if they want to keep holding hands, they would have to stop their spins shortly thereafter.
A: 
Astronaut A pulls with her right hand B's left hand toward herself. While at the same time, B pulls on A using her right hand to draw A's left hand toward herself.

Notice that both astronauts move closer to each other on both sides, since both pull with their right hands and are pulled by their left hands. Assuming rigid (and symmetric and identical) astronauts, they don't twist or spin, but simply accelerate into each other face to face. A generates a clockwise torque on B, but the reaction force causes a counterclockwise torque on A. Meanwhile B is generating a clockwise torque on A (canceling out the CCW torque A generates by pulling B) and that reaction generates a counterclockwise torque on B, canceling out the original CW torque caused by A's pull. Each astronaut experiences a net zero torque, and thus no net change in angular momentum: and if the angular momentum of each astronaut stays the same, then so does the angular momentum of the entire system.
A: With the astronauts, there are two general ways to contribute to the angular motion of the system: the motion of the astronaut's center of mass around the axis in question, and the spin of the astronaut around their own center of mass.
So it's quite possible for the system to begin at rest ($L=0$), and through internal forces start things spinning.  The astronauts may start moving around this axis clockwise with some angular momentum $L$.  If so, then they will be rotating counterclockwise with some angular momentum $-L$.  The total momentum is conserved.
